# Richter magnitude scale

The Richter magnitude scale (often shortened to Richter scale) was developed to assign a single number to quantify the energy released during an earthquake.

The scale is a base-10 logarithmic scale. The magnitude is defined as the logarithm of the ratio of the amplitude of waves measured by a seismograph to an arbitrary small amplitude. An earthquake that measures 5.0 on the Richter scale has a shaking amplitude 10 times larger than one that measures 4.0, and corresponds to a 31.6 times larger release of energy.[1]

Since the mid-20th century, the use of the Richter magnitude scale has largely been supplanted by the moment magnitude scale (MMS) in many countries. However, the Richter scale is still widely used in Russia and other CIS countries. Earthquake measurements under the moment magnitude scale in the United States—3.5 and up, on the MMS scale—are still usually erroneously referred to as being quoted on the Richter scale by the general public, as well as the media, due to their familiarity with the Richter scale as opposed to the MMS.

## Development

Charles Richter, c. 1970

Developed in 1935 by Charles Francis Richter in partnership with Beno Gutenberg, both from the California Institute of Technology, the scale was firstly intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismograph. Richter originally reported values to the nearest quarter of a unit, but values were later reported with one decimal place. His motivation for creating the local magnitude scale was to compare the size of different earthquakes.[1] Richter, who since childhood had aspirations in astronomy, drew inspiration from the apparent magnitude scale used to account for the brightness of stars lost due to distance.[2] Richter arbitrarily chose a magnitude 0 event to be an earthquake that would show a maximum combined horizontal displacement of 1 µm (0.00004 in) on a seismogram recorded using a Wood-Anderson torsion seismograph 100 km (62 mi) from the earthquake epicenter. This choice was intended to prevent negative magnitudes from being assigned. The smallest earthquakes that could be recorded and located at the time were around magnitude 3. However, the Richter scale has no lower limit, and sensitive modern seismographs now routinely record quakes with negative magnitudes.

ML (local magnitude) was not designed to be applied to data with distances to the hypocenter of the earthquake greater than 600 km[3] (373 mi). For national and local seismological observatories the standard magnitude scale is today still ML. Unfortunately this scale saturates[clarification needed] at around ML = 7,[4] because the high frequency waves recorded locally have wavelengths shorter than the rupture lengths[clarification needed] of large earthquakes.

To express the size of earthquakes around the globe, Gutenberg and Richter later developed a magnitude scale based on surface waves, surface wave magnitude Ms; and another based on body waves, body wave magnitude mb.[5] These are types of waves that are recorded at teleseismic distances. The two scales were adjusted such that they were consistent with the ML scale. This succeeded better with the Ms scale than with the mb scale. Both of these scales saturate when the earthquake is bigger than magnitude 8 and therefore the moment magnitude scale, Mw, was invented.[6]

These older magnitude scales have been superseded by methods for estimating the seismic moment, creating the moment magnitude scale, although the older scales are still widely used because they can be calculated quickly.

I found a paper by Professor K. Wadati of Japan in which he compared large earthquakes by plotting the maximum ground motion against distance to the epicenter. I tried a similar procedure for our stations, but the range between the largest and smallest magnitudes seemed unmanageably large. Dr. Beno Gutenberg then made the natural suggestion to plot the amplitudes logarithmically. I was lucky because logarithmic plots are a device of the devil.

## Details

The Richter scale proper was defined in 1935 for particular circumstances and instruments; the instrument used saturated for strong earthquakes. The scale was replaced by the moment magnitude scale (MMS); for earthquakes adequately measured by the Richter scale, numerical values are approximately the same. Although values measured for earthquakes now are actually $M_w$ (MMS), they are frequently reported as Richter values, even for earthquakes of magnitude over 8, where the Richter scale becomes meaningless. Anything above 5 is classified as a risk by the USGS.[citation needed]

The Richter and MMS scales measure the energy released by an earthquake; another scale, the Mercalli intensity scale, classifies earthquakes by their effects, from detectable by instruments but not noticeable to catastrophic. The energy and effects are not necessarily strongly correlated; a shallow earthquake in a populated area with soil of certain types can be far more intense than a much more energetic deep earthquake in an isolated area.

There are several scales which have historically been described as the "Richter scale," especially the local magnitude $M_L$ and the surface wave $M_s$ scale. In addition, the body wave magnitude, $m_b$, and the moment magnitude, $M_w$, abbreviated MMS, have been widely used for decades, and a couple of new techniques to measure magnitude are in the development stage.

All magnitude scales have been designed to give numerically similar results. This goal has been achieved well for $M_L$, $M_s$, and $M_w$.[7][8] The $m_b$ scale gives somewhat different values than the other scales. The reason for so many different ways to measure the same thing is that at different distances, for different hypocentral depths, and for different earthquake sizes, the amplitudes of different types of elastic waves must be measured.

$M_L$ is the scale used for the majority of earthquakes reported (tens of thousands) by local and regional seismological observatories. For large earthquakes worldwide, the moment magnitude scale is most common, although $M_s$ is also reported frequently.

The seismic moment, $M_o$, is proportional to the area of the rupture times the average slip that took place in the earthquake, thus it measures the physical size of the event. $M_w$ is derived from it empirically as a quantity without units, just a number designed to conform to the $M_s$ scale.[9] A spectral analysis is required to obtain $M_o$, whereas the other magnitudes are derived from a simple measurement of the amplitude of a specifically defined wave.

All scales, except $M_w$, saturate for large earthquakes, meaning they are based on the amplitudes of waves which have a wavelength shorter than the rupture length of the earthquakes. These short waves (high frequency waves) are too short a yardstick to measure the extent of the event. The resulting effective upper limit of measurement for $M_L$ is about 7[4] and about 8.5[4] for $M_s$.[10]

New techniques to avoid the saturation problem and to measure magnitudes rapidly for very large earthquakes are being developed. One of these is based on the long period P-wave,[11] the other is based on a recently discovered channel wave.[12]

The energy release of an earthquake,[13] which closely correlates to its destructive power, scales with the 32 power of the shaking amplitude. Thus, a difference in magnitude of 1.0 is equivalent to a factor of 31.6 ($=({10^{1.0}})^{(3/2)}$) in the energy released; a difference in magnitude of 2.0 is equivalent to a factor of 1000 ($=({10^{2.0}})^{(3/2)}$ ) in the energy released.[14] The elastic energy radiated is best derived from an integration of the radiated spectrum, but one can base an estimate on $m_b$ because most energy is carried by the high frequency waves.

## Richter magnitudes

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the variation in the distance between the various seismographs and the epicenter of the earthquake). The original formula is:[15]

$M_\mathrm{L} = \log_{10} A - \log_{10} A_\mathrm{0}(\delta) = \log_{10} [A / A_\mathrm{0}(\delta)],\$

where A is the maximum excursion of the Wood-Anderson seismograph, the empirical function A0 depends only on the epicentral distance of the station, $\delta$. In practice, readings from all observing stations are averaged after adjustment with station-specific corrections to obtain the ML value.

Because of the logarithmic basis of the scale, each whole number increase in magnitude represents a tenfold increase in measured amplitude; in terms of energy, each whole number increase corresponds to an increase of about 31.6 times the amount of energy released, and each increase of 0.2 corresponds to a doubling of the energy released.

Events with magnitudes greater than 4.5 are strong enough to be recorded by a seismograph anywhere in the world, so long as its sensors are not located in the earthquake's shadow.

The following describes the typical effects of earthquakes of various magnitudes near the epicenter. The values are typical only and should be taken with extreme caution, since intensity and thus ground effects depend not only on the magnitude, but also on the distance to the epicenter, the depth of the earthquake's focus beneath the epicenter, the location of the epicenter and geological conditions (certain terrains can amplify seismic signals).

MagnitudeDescriptionMercalli intensityAverage earthquake effectsAverage frequency of occurrence (estimated)
Less than 2.0MicroIMicroearthquakes, not felt, or felt rarely by sensitive people. Recorded by seismographs.[16]Continual/several million per year
2.0–2.9MinorI to IIFelt slightly by some people. No damage to buildings.Over one million per year
3.0–3.9II to IVOften felt by people, but very rarely causes damage. Shaking of indoor objects can be noticeable.Over 100,000 per year
4.0–4.9LightIV to VINoticeable shaking of indoor objects and rattling noises. Felt by most people in the affected area. Slightly felt outside. Generally causes none to minimal damage. Moderate to significant damage very unlikely. Some objects may fall off shelves or be knocked over.10,000 to 15,000 per year
5.0–5.9ModerateVI to VIIICan cause damage of varying severity to poorly constructed buildings. At most, none to slight damage to all other buildings. Felt by everyone. Casualties range from none to a few.1,000 to 1,500 per year
6.0–6.9StrongVII to XDamage to a moderate number of well built structures in populated areas. Earthquake-resistant structures survive with slight to moderate damage. Poorly-designed structures receive moderate to severe damage. Felt in wider areas; up to hundreds of miles/kilometers from the epicenter. Strong to violent shaking in epicentral area. Death toll ranges from none to 25,000.100 to 150 per year
7.0–7.9MajorVIII or greater[17]Causes damage to most buildings, some to partially or completely collapse or receive severe damage. Well-designed structures are likely to receive damage. Felt across great distances with major damage mostly limited to 250 km from epicenter. Death toll ranges from none to 250,000.10 to 20 per year
8.0–8.9GreatMajor damage to buildings, structures likely to be destroyed. Will cause moderate to heavy damage to sturdy or earthquake-resistant buildings. Damaging in large areas. Felt in extremely large regions. Death toll ranges from 1,000 to 1 million.One per year
9.0 and greaterNear or at total destruction - severe damage or collapse to all buildings. Heavy damage and shaking extends to distant locations. Permanent changes in ground topography. Death toll usually over 50,000.One per 10 to 50 years

(Based on U.S. Geological Survey documents.)[18]

The intensity and death toll depend on several factors (earthquake depth, epicenter location, population density, to name a few) and can vary widely.

Minor earthquakes occur every day and hour. On the other hand, great earthquakes occur once a year, on average. The largest recorded earthquake was the Great Chilean Earthquake of May 22, 1960, which had a magnitude of 9.5 on the moment magnitude scale.[19] The larger the magnitude, the less frequent the earthquake happens.

### Examples

The following table lists the approximate energy equivalents in terms of TNT explosive force – though note that the earthquake energy is released underground rather than overground.[20] Most energy from an earthquake is not transmitted to and through the surface; instead, it dissipates into the crust and other subsurface structures. In contrast, a small atomic bomb blast (see nuclear weapon yield) will not, it will simply cause light shaking of indoor items, since its energy is released above ground.

31.6227 to the power of 0 equals 1, 31.6227 to the power of 1 equals 31.6227 and 31.6227 to the power of 2 equals 1000. Therefore, an 8.0 on the Richter scale releases 31.6227 times more energy than a 7.0 and a 9.0 on the Richter scale releases 1000 times more energy than a 7.0. Thus, $E \approx 6.3\times 10^4\times 10^{3M/2}\,$

Approximate MagnitudeApproximate TNT for
Seismic Energy Yield
Joule equivalentExample
0.015 g63 kJ
0.585 g360 kJ
1.0480 g2.0 MJ
1.21.1 kg4.9 MJSingle stick of dynamite [DynoMax Pro]
1.42.2 kg9.8 MJSeismic impact of typical small construction blast
1.52.7 kg11 MJ
2.015 kg63 MJ
2.121 kg89 MJWest fertilizer plant explosion[21]
2.585 kg360 MJ
3.0480 kg2.0 GJOklahoma City bombing, 1995
3.52.7 metric tons11 GJPEPCON fuel plant explosion, Henderson, Nevada, 1988

Dallas, Texas earthquake, September 30, 2012

3.879.5 metric tons40 GJExplosion at Chernobyl nuclear power plant, 1986
3.9111 metric tons46 GJMassive Ordnance Air Blast bomb

St. Patrick's Day earthquake, Auckland, New Zealand, 2013 [22][23]

4.015 metric tons63 GJJohannesburg/South Africa, November 18, 2013
4.343 metric tons180 GJKent Earthquake (Britain), 2007

Eastern Kentucky earthquake, November 2012

5.0480 metric tons2.0 TJLincolnshire earthquake (UK), 2008
5.52.7 kilotons11 TJLittle Skull Mtn. earthquake (Nevada, USA), 1992
5.63.8 kilotons16 TJNewcastle, Australia, 1989
6.015 kilotons63 TJDouble Spring Flat earthquake (Nevada, USA), 1994

Approximate magnitude of Virginia/Washington, D.C./East Coast earthquake, 2011
Approximate yield of the Little Boy Atomic Bomb dropped on Hiroshima (~16 kt)

6.343 kilotons180 TJ$M_W$ Rhodes earthquake (Greece), 2008
6.460 kilotons250 TJKaohsiung earthquake (Taiwan), 2010

6.585 kilotons360 TJ$M_S$ Caracas earthquake (Venezuela), 1967

Irpinia earthquake (Italy), 1980
$M_W$ Eureka earthquake (California, USA), 2010
Zumpango del Rio earthquake (Guerrero, Mexico), 2011[26]

6.6120 kilotons500 TJ$M_W$ San Fernando earthquake (California, USA), 1971
6.7170 kilotons710 TJ$M_W$ Northridge earthquake (California, USA), 1994
6.8240 kilotons1.0 PJ$M_W$ Nisqually earthquake (Anderson Island, WA), 2001
6.9340 kilotons1.4 PJ$M_W$ San Francisco Bay Area earthquake (California, USA), 1989
7.0480 kilotons2.0 PJ$M_W$ Java earthquake (Indonesia), 2009
7.1680 kilotons2.8 PJ$M_W$ Messina earthquake (Italy), 1908
7.2950 kilotons4.0 PJVrancea earthquake (Romania), 1977
7.52.7 megatons11 PJ$M_W$ Kashmir earthquake (Pakistan), 2005
7.63.8 megatons16 PJ$M_W$ Nicoya earthquake (Costa Rica), 2012
7.75.4 megatons22 PJ$M_W$ Sumatra earthquake (Indonesia), 2010
7.87.6 megatons32 PJ$M_W$ Tangshan earthquake (China), 1976
7.910-15 megatons42-63 PJTunguska event
1802 Vrancea earthquake
8.015 megatons63 PJ$M_S$ Mino-Owari earthquake (Japan), 1891
8.121 megatons89 PJMéxico City earthquake (Mexico), 1985

Guam earthquake, August 8, 1993[27]

8.3550 megatons210 PJTsar Bomba - Largest thermonuclear weapon ever tested
8.585 megatons360 PJ$M_W$ Sumatra earthquake (Indonesia), 2007
8.6120 megatons500 PJ$M_W$ Sumatra earthquake (Indonesia), 2012
8.7170 megatons710 PJ$M_W$ Sumatra earthquake (Indonesia), 2005
8.75200 megatons840 PJKrakatoa 1883
8.8240 megatons1.0 EJ$M_W$ Chile earthquake, 2010,
9.0480 megatons2.0 EJ$M_W$ Lisbon earthquake (Portugal), All Saints Day, 1755
$M_W$ The Great Japan earthquake, March 2011
9.15800 megatons3.3 EJToba eruption 75,000 years ago; among the largest known volcanic events.[28]
9.2950 megatons4.0 EJ$M_W$ Anchorage earthquake (Alaska, USA), 1964
$M_W$ Sumatra-Andaman earthquake and tsunami (Indonesia), 2004
9.52.7 gigatons11 EJ$M_W$ Valdivia earthquake (Chile), 1960
10.015 gigatons63 EJNever recorded, equivalent to an earthquake rupturing a very large, lengthy fault, or an extremely rare/impossible mega-earthquake, shown in science fiction[clarification needed]
12.55100 teratons420 ZJYucatán Peninsula impact (creating Chicxulub crater) 65 Ma ago (108 megatons; over 4x1029 ergs = 400 ZJ).[29][30][31][32][33]
22.88 or 32310 yottatons1.3×1039 JApproximate magnitude of the starquake on the magnetar SGR 1806-20, registered on December 27, 2004.[clarification needed]

## Magnitude empirical formula

These formula are an alternative method to calculate Richter magnitude instead of using Richter correlation tables based on Richter standard seismic event ($M_\mathrm{L}$=0, A=0.001mm, D=100 km).

The Lillie empirical formula:

$M_\mathrm{L} = \log_{10}A - 2.48+ 2.76\log_{10}\Delta$

Where:

• A is the amplitude (maximum ground displacement) of the P-wave, in micrometers, measured at 0.8 Hz.
• $\Delta$ is the epicentral distance, in km.

For distance less than 200 km:

$M_\mathrm{L} = \log_{10} A + 1.6\log_{10} D - 0.15$

For distance between 200 km and 600 km:

$M_\mathrm{L} = \log_{10} A + 3.0\log_{10} D - 3.38$

where A is seismograph signal amplitude in mm, D distance in km.

The Bisztricsany (1958) empirical formula for epicentral distances between 4˚ to 160˚:

$M_\mathrm{L} = 2.92 + 2.25 \log_{10} (\tau) - 0.001 \Delta^{\circ}$

Where:

• $M_\mathrm{L}$ is magnitude (mainly in the range of 5 to 8)
• $\tau$ is the duration of the surface wave in seconds
• $\Delta$ is the epicentral distance in degrees.

The Tsumura empirical formula:

$M_\mathrm{L} = -2.53 + 2.85 \log_{10} (F-P) + 0.0014 \Delta^{\circ}$

Where:

• $M_\mathrm{L}$ is the magnitude (mainly in the range of 3 to 5).
• $F-P$ is the total duration of oscillation in seconds.
• $\Delta$ is the epicentral distance in kilometers.

The Tsuboi, University of Tokio, empirical formula:

$M_\mathrm{L} = \log_{10}A + 1.73\log_{10}\Delta - 0.83$

Where:

• $M_\mathrm{L}$ is the magnitude.
• $A$ is the amplitude in um.
• $\Delta$ is the epicentral distance in kilometers.

 Earthquakes portal

## References

1. ^ a b The Richter Magnitude Scale
2. ^ Reitherman, Robert (2012). Earthquakes and Engineers: An International History. Reston, VA: ASCE Press. pp. 208–209. ISBN 9780784410714.
3. ^ "USGS Earthquake Magnitude Policy". USGS. March 29, 2010.
4. ^ a b c http://www.weather.gov.hk/education/edu02rga/article/ele-EarthquakeMagnetude_e.htm
5. ^ William L. Ellsworth (1991). SURFACE-WAVE MAGNITUDE (Ms) AND BODY-WAVE MAGNITUDE (mb). USGS. Retrieved 2008-09-14.
6. ^ Kanamori
7. ^ Richter, C.F. (1935). "An instrumental earthquake magnitude scale". Bulletin of the Seismological Society of America 25 (1-2): 1–32.
8. ^ Richter, C.F., "Elementary Seismology", edn, Vol., W. H. Freeman and Co., San Francisco, 1956.
9. ^ Hanks, T. C. and H. Kanamori, 1979, "Moment magnitude scale", Journal of Geophysical Research, 84, B5, 2348.
10. ^ "Richter scale". Glossary. USGS. March 31, 2010.
11. ^ Di Giacomo, D., Parolai, S., Saul, J., Grosser, H., Bormann, P., Wang, R. & Zschau, J., 2008. Rapid determination of the enrgy magnitude Me, in European Seismological Commission 31st General Assembly, Hersonissos.
12. ^ Rivera, L. & Kanamori, H., 2008. Rapid source inversion of W phase for tsunami warning, in European Geophysical Union General Assembly, pp. A-06228, Vienna.
13. ^ Marius Vassiliou and Hiroo Kanamori (1982): "The Energy Release in Earthquakes," Bull. Seismol. Soc. Am. 72, 371-387.
14. ^ USGS: Measuring the Size of an Earthquake, Section 'Energy, E'
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16. ^ This is what Richter wrote in his Elementary Seismology (1958), an opinion copiously reproduced afterwards in Earth's science primers. Recent evidence shows that earthquakes with negative magnitudes (down to −0.7) can also be felt in exceptional cases, especially when the focus is very shallow (a few hundred metres). See: Thouvenot, F.; Bouchon, M. (2008). What is the lowest magnitude threshold at which an earthquake can be felt or heard, or objects thrown into the air?, in Fréchet, J., Meghraoui, M. & Stucchi, M. (eds), Modern Approaches in Solid Earth Sciences (vol. 2), Historical Seismology: Interdisciplinary Studies of Past and Recent Earthquakes, Springer, Dordrecht, 313–326.
17. ^
18. ^ [1]
19. ^ USGS: List of World's Largest Earthquakes
20. ^ FAQs – Measuring Earthquakes
21. ^ http://earthquake.usgs.gov/earthquakes/eventpage/usb000g9yl#summary
22. ^ http://www.geonet.org.nz/quakes/region/aucklandnorthland/2013p203051
23. ^ http://www.nzherald.co.nz/nz/news/article.cfm?c_id=1&objectid=10871821
24. ^ "Magnitude 5.0 – Ontario-Quebec border region, Canada". earthquake.usgs.gov. Retrieved 2010-06-23.
25. ^ "Moderate 5.0 earthquake shakes Toronto, Eastern Canada and U.S.". nationalpost.com. Retrieved 2010-06-23.
26. ^ "Past Earthquakes" (in Spanish). Servicio Sismologico Nacional. Retrieved 2 March 2013.
27. ^ "M8.1 South End of Island August 8, 1993.". eeri.org. Retrieved 2011-03-11..
28. ^ Petraglia, M.; R. Korisettar, N. Boivin, C. Clarkson,4 P. Ditchfield,5 S. Jones,6 J. Koshy,7 M.M. Lahr,8 C. Oppenheimer,9 D. Pyle,10 R. Roberts,11 J.-C. Schwenninger,12 L. Arnold,13 K. White. (6 July 2007). "Middle Paleolithic Assemblages from the Indian Subcontinent Before and After the Toba Super-eruption". Science 317 (5834): 114–116. doi:10.1126/science.1141564. PMID 17615356.
29. ^ Bralower, Timothy J.; Charles K. Paull; R. Mark Leckie (1998). "The Cretaceous-Tertiary boundary cocktail: Chicxulub impact triggers margin collapse and extensive sediment gravity flows". Geology 26: 331–334. Bibcode:1998Geo....26..331B. doi:10.1130/0091-7613(1998)026<0331:TCTBCC>2.3.CO;2. ISSN 0091-7613. Retrieved 2009-09-03.
30. ^ Klaus, Adam; Norris, Richard D.; Kroon, Dick; Smit, Jan (2000). "Impact-induced mass wasting at the K-T boundary: Blake Nose, western North Atlantic". Geology 28: 319–322. Bibcode:2000Geo....28..319K. doi:10.1130/0091-7613(2000)28<319:IMWATK>2.0.CO;2. ISSN 0091-7613. Unknown parameter |unused_data= ignored (help);
31. ^ Busby, Cathy J.; Grant Yip; Lars Blikra; Paul Renne (2002). "Coastal landsliding and catastrophic sedimentation triggered by Cretaceous-Tertiary bolide impact: A Pacific margin example?". Geology 30: 687–690. Bibcode:2002Geo....30..687B. doi:10.1130/0091-7613(2002)030<0687:CLACST>2.0.CO;2. ISSN 0091-7613.
32. ^ Simms, Michael J. (2003). "Uniquely extensive seismite from the latest Triassic of the United Kingdom: Evidence for bolide impact?". Geology 31: 557–560. Bibcode:2003Geo....31..557S. doi:10.1130/0091-7613(2003)031<0557:UESFTL>2.0.CO;2. ISSN 0091-7613.
33. ^ Simkin, Tom; Robert I. Tilling; Peter R. Vogt; Stephen H. Kirby; Paul Kimberly; David B. Stewart (2006). "This dynamic planet. World map of volcanoes, earthquakes, impact craters, and plate tectonics. Inset VI. Impacting extraterrestrials scar planetary surfaces". U.S. Geological Survey. Retrieved 2009-09-03.